Arithmetic and Combinatorics: Kant and His Contemporaries

By Gottfried Martin; Judy Wubnig | Go to book overview

Subject Index
Abstraction, 93, 111
Académie des Sciences, Paris,xxv, 145
Actuality, 78
Addition, 40, 42, 53, 90, 94, 99, 101, 103-5, 108, 113-14, 123, 130-34, 136; associative law of, 15, 25, 50, 54; axioms of, 34; as basis of all mathematics, 130; commutative law of, 15, 25, 50, 54; concept of, 41, 44; of large numbers, 98; laws of, 35, 43, 44; and memory, 88; of negative numbers, 54; postulates of, 36; properties of, 43; rules of, 43, 98; of small numbers, 97; successive, 85, 86, 109, 137; as synthetic, 135; unlimited feasibility of, 35; unlimited increase, 36
Ad infinitum, 56-57
Ad intuitum, 107
Aerometrics, aerometry, 143-44
Aesthetic, transcendental, 85, 100
Aitemata, 146
Alchemists, 67, 76
Algebra, 38, 68, 83, 92, 93, 131, 137, 143, 151; algebraist, 134-35, 164; and equations, 57, 58; methods of, 60; and numbers, 58; propositions of, 49, 132
Algorithm, 42-43
Allness, 86
Analysis, 20, 57, 92, 97, 99, 104; a priori, 80; concept of 7 + 5, 137; and concepts, 95, 107, 132, 137; and counting, 89; elementary propositions of, 29; infinite, 132
Analytic-synthetic, 27, 28, 111, 129, 145
Angles: of contact, 53; right, 31; triangle, 112
Animal rationale, 96-97
Appearance, 28, 91, 118
Apperception, 89, 90, 91, 92
Apprehension, synthesis, 88
A priori, apriorizing, 82, 123
Architecture, 143
Arithmetic, xviii, xxi, xxiv, 6, 9, 14, 26, 36, 39, 42-43, 45, 48-50, 56, 60, 81, 83, 85, 91-94, 97-102, 104-10, 112, 115, 119, 123-25, 130-38, 143, 144, 145, 150, 159; analytic, 114, 132; axioms of, xviii, 4, 25, 26, 29, 37, 39, 40, 44, 49, 100-6, 109, 133, 136-38; concepts of, 91, 118; constructive, 6; demonstrations, 47; elementary, 131, 133, 135; expansion of, 101; general, 4, 24, 38, 106; and geometry, 8, 25, 145; higher, 93, 131, 133, 135; laws of, 35, 44, 123; and logic, xviii, 6-7, 119; and logicism, xviii, 6; methods of, 60, 118; operations of, 47, 124; postulates of, 5, 36-37, 49, 102, 135-138; principles of, 24-25, 29, 35, 48, 122; synthetic, 101, 103-6, 110, 161; theorems of, xviii
Arithmetization: mathematics, 92; of numbers, 87, 92-93
Ars characteristica, 60
Artillery, xxiv, 143
Association: addition,15, 25, 35, 44, 50, 54, 96, 101, 114, 118-19, 123; algorithm, 42, 43; axiom, 106; logistic, 115-16
Assumption, a priori, 75
Astronomy, xxvi, 110, 129, 143, 145
Attributes, 62, 63
Axiomata, 28, 29
Axiomatic: foundation, 45, 101; geometry, 145; and Iogicist, 145; method, 15, 114; principles, 28; school, xvii; science, 99; view, 6-7, 13, 99
Axiomatics, 9, 12, 39, 40, 53, 116, 124; systematic, 14, 39
Axioms, 6, 9, 11-15, 16, 19,20, 32, 35-37,

-191-

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Arithmetic and Combinatorics: Kant and His Contemporaries
Table of contents

Table of contents

  • Title Page iii
  • Contents v
  • Foreword vii
  • Translator's Preface xi
  • Preface [1938] xv
  • Introduction xvii
  • Part I 1
  • Chapter One - The Axiomatics and Logic of Mathematics 3
  • Chapter Two - The Analytic Principles 11
  • Chapter Three - The Axioms of Arithmetic 34
  • Part II 51
  • Chapter Four - Problems About Classes of Numbers 53
  • Chapter Five - Combinatorics and the Idea of A Systematic Ontology 59
  • Chapter Six - Synthetic Judgment in Arithmetic 85
  • Appendix - Examination of Kant's "Critique of Pure Reason," Part I, Section 4 129
  • Notes 141
  • Bibliography 165
  • Name Index 185
  • Subject Index 191
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